Shareholders allege director Marc Andreessen privately coached the CEO by text message on how to win over other members of the board

Facebook Inc.’s move to change its capital structure was tainted by secret text messages and meddling from financial advisers that pointed to a process rife with conflicts of interest, according to investor lawsuits filed in Delaware.

Late last summer, Chief Executive Mark Zuckerberg asked the board to approve a plan to create a new class of nonvoting shares that would allow him to maintain control of the company he co-founded. The...